Variational Theories in Hydrodynamics and Hydraulics
Publication: Journal of Hydraulic Engineering
Volume 120, Issue 6
Abstract
Hydrodynamic and hydraulic theories have been developed along two parallel approaches, i.e., the vectorial and variational approaches. Most classical hydraulic theories are based on vectorial approaches. The variational approach is a scalar approach based on the maximization of entropy, minimization of energy, or minimization of energy dissipation rate. A review of variational theories and hypotheses shows that fundamental theories in hydrodynamics and hydraulics derived from vectorial approaches can also be independently derived from variational approaches. A comparison of different variational theories indicates that they are consistent with each other provided that the concepts of entropy and energy are properly defined and correctly applied.
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References
1.
Chapman, T. G. (1986). “Entropy as a measure of hydrologic data uncertainty and model performance.” J. of Hydro., Vol. 85, 115–126.
2.
Chiu, C. L. (1987). “Entropy and probability concepts in hydraulics.” J. Hydr. Engrg., ASCE, 113(5), 583–600.
3.
Chiu, C. L. (1988). “Entropy and 2D velocity distribution in open channels.” J. Hydr. Engrg., ASCE, 114(7), 738–756.
4.
Chiu, C. L. (1989). “Velocity distribution in open channel flow.” J. Hydr. Engrg., ASCE, 115(5), 576–594.
5.
Chiu, C. L. (1991). “Application of entropy concept in open channel flow study.” J. Hydr. Engrg., ASCE, 117(5), 615–628.
6.
Chiu, C. L. (1992). “Applications of probability and entropy concepts in open channel hydraulics.” Entropy and energy dissipation in water resources, V. P. Singh and M. Fiorentino, eds., Kluwel Academic Publishers, London, United Kingdom, 321–341.
7.
Chiu, C. L., Lin, G. G., and Lu, J. M. (1993). “Application of probability and entropy concepts in pipe‐flow studies.” J. Hydr. Engrg., ASCE, 119(6), 743–756.
8.
Davis, T. R. H., and Sutherland, A. J. (1983). “Extremal hypotheses for river behavior.” Water Resour. Res., 19(1), 141–148.
9.
Gyarmati, I.(1968). “On the governing principle of dissipative processes and its extension to nonlinear problems.” Ann. Phys. 7, 23.
10.
Gyarmati, I. (1970). Nonequilibrium Thermodynamics. Springer‐Verlag, Berlin, Germany.
11.
Hadley, G. (1964). Nonlinear and dynamic programming. Addison‐Wesley Publication Co., San Diego, Calif.
12.
Hou, H. C., and Kuo, J. R. (1987). “Gyarmati principle and open‐channel velocity distribution.” J. Hydr. Engrg., 113(5), 563–572.
13.
Jaynes, E. T. (1957a). “Information theory and statistical mechanics.” Physical Rev., 106(4), 620–630.
14.
Jaynes, E. T. (1957b). “Information theory and statistical mechanics II.” Physical Rev., 108(2), 171–190.
15.
Kennedy, J. F., Richardson, P. D., and Sutera, S. P. (1964). “Discussion of ‘Geometry of river channels,’ by W. B. Langbein.” J. Hydr. Div., ASCE, 90(6), 332–341.
16.
Langbein, W. B. (1964). “Geometry of river channels.” ASCE Proc., ASCE, New York, N.Y., Vol. 90, 301–312.
17.
Leopold, L. B., and Maddock Jr., T. (1953). “The hydraulic geometry of stream channels and some physiographic implications.” U.S. Geological Survey (USGS) Prof. Paper 252, USGS, Washington, D.C.
18.
Leopold, L. B., and Langbein, W. B. (1962). “The concept of entropy in landscape evolution.” U.S. Geological Survey Professional Paper No. 500‐A, Washington, D.C.
19.
Lewis, G. N., and Randall, M. (1961). Thermodynamics, 2nd Ed., revised by K. S. Pitzer and L. Brewer, McGraw‐Hill, New York, N.Y.
20.
Li, J. C. M. (1962). “Thermodynamics for nonequilibrium systems, the principle of macroscopic separability and the thermodynamic potential.” J. Appl. Phys., Vol. 33.
21.
Prigogin, I. (1967). Introduction to thermodynamics of irreversible processes, 3rd Ed., John Wiley & Sons, New York, N.Y.
22.
Ramette, M. (1980). “A theoretical approval on fluvial processes.” Proc., Int. Symp. on River Sedimentation, Beijing, China, 601–618.
23.
Ramette, M. (1981). “Guide to river engineering.” Rep. He/40/81.04, State Electricity Commission of Victoria, Electricité de France, Direction des Etudes et Recherches.
24.
Shannon, C. E. (1948). “A mathematical theory of communication.” The Bell System Tech. J., XXVII(3), 379–656.
25.
Scheidegger, A. E. (1964). “Some implications of statistical mechanics in geomorphology.” Bull. of the Int. Assoc. of Scientific Hydro., IX(1), 12–16.
26.
Singh, V. P., and Fiorentino, M. (1992). “A historical perspective of entropy applications in water resources.” Entropy and energy dissipation in water resources, V. P. Singh and M. Fiorentino, eds., Kluwer Academic Publishers, London, United Kingdom, 21–61.
27.
White, W. R., Bettes, R., and Paris, E. (1982). “Analytical approach to river regime.” J. Hydr. Div., 108(10), 1179–1193.
28.
Williams, G. P. (1978). “Hydraulic geometry of river cross sections—theory of minimum variance.” U.S. Geological Survey, Prof. Paper 1029, USGS, Washington, D.C.
29.
Wilson, A. G. (1970). “The use of the concept of entropy in system modelling.” Operational Res. Quarterly, 21(2), 247–265.
30.
Verhás, J. (1967). “Deduction of transport equations from the integral principle of hermodynamics.” Zeitschrift fur Physikalische Chemie (Hungary), Vol. 234.
31.
Yang, C. T. (1971). “Potential energy and stream morphology.” Water Resour. Res., 7(2), 311–322.
32.
Yang, C. T. (1983). “Minimum rate of energy dissipation and river morphology.” Proc., D. B. Simons Symp. on Erosion and Sedimentation, R. M. Li and P. F. Lagassee, eds., Colorado State University, 3.2–3.19.
33.
Yang, C. T. (1992). “Force, energy, entropy, and energy dissipation rate.” Entropy and energy dissipation in water resources, V. P. Singh and M. Fiorentino, eds., Kluwer Academic Publishers, London, United Kingdom, 63–89.
34.
Yang, C. T., and Molinas, A. (1988). “Dynamic adjustment of channel width and slope.” Proc., Int. Conf. on River Regime, W. R. White, ed., John Wiley & Sons, 17–28.
35.
Yang, C. T., and Song, C. C. S. (1986). “Chapter 11: theory of minimum energy and energy dissipation rate.” Encyclopedia of fluid mechanics, Vol. 1, N. P. Cheremisinoff, ed., Gulf Publishing Co., Houston, Tex., 353–399.
36.
Yourgrau, W., and Mandelstam, S. (1968). Variational principles in dynamics and quantum theory. Dover Publication, Inc., New York, N.Y.
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Copyright © 1994 American Society of Civil Engineers.
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Received: Oct 12, 1993
Published online: Jun 1, 1994
Published in print: Jun 1994
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